Charge Disproportionation without Charge Transfer in the Rare-Earth-Element Nickelates as a Possible Mechanism for the Metal-Insulator Transition

We study a model for the metal-insulator (M-I) transition in the rare-earth-element nickelates RNiO3, based upon a negative charge transfer energy and coupling to a rocksaltlike lattice distortion of the NiO6 octahedra. Using exact diagonalization and the Hartree-Fock approximation we demonstrate that electrons couple strongly to these distortions. For small distortions the system is metallic, with a ground state of predominantly d(8)L character, where (L) under bar denotes a ligand hole. For sufficiently large distortions (delta d(Ni-O) similar to 0.05-0.10 angstrom), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with (d(8)(L) under bar (2))(S=0)(d(8))(S=1) character, where S is the total spin. Thus the M-I transition may be viewed as being driven by an internal volume "collapse" where the NiO6 octahedra with two ligand holes shrink around their central Ni, while the remaining octahedra expand accordingly, resulting in the (1/2, 1/2, 1/2) superstructure observed in x-ray diffraction in the insulating phase. This insulating state is an example of charge ordering achieved without any actual movement of the charge.